Problem: $\dfrac{ -5h + 2i }{ -10 } = \dfrac{ 7h - 10j }{ -7 }$ Solve for $h$.
Answer: Multiply both sides by the left denominator. $\dfrac{ -5h + 2i }{ -{10} } = \dfrac{ 7h - 10j }{ -7 }$ $-{10} \cdot \dfrac{ -5h + 2i }{ -{10} } = -{10} \cdot \dfrac{ 7h - 10j }{ -7 }$ $-5h + 2i = -{10} \cdot \dfrac { 7h - 10j }{ -7 }$ Multiply both sides by the right denominator. $-5h + 2i = -10 \cdot \dfrac{ 7h - 10j }{ -{7} }$ $-{7} \cdot \left( -5h + 2i \right) = -{7} \cdot -10 \cdot \dfrac{ 7h - 10j }{ -{7} }$ $-{7} \cdot \left( -5h + 2i \right) = -10 \cdot \left( 7h - 10j \right)$ Distribute both sides $-{7} \cdot \left( -5h + 2i \right) = -{10} \cdot \left( 7h - 10j \right)$ ${35}h - {14}i = -{70}h + {100}j$ Combine $h$ terms on the left. ${35h} - 14i = -{70h} + 100j$ ${105h} - 14i = 100j$ Move the $i$ term to the right. $105h - {14i} = 100j$ $105h = 100j + {14i}$ Isolate $h$ by dividing both sides by its coefficient. ${105}h = 100j + 14i$ $h = \dfrac{ 100j + 14i }{ {105} }$